Electrodialysis 0D lacks a membrane resistance term in resistance calculation

[yschang23]

Description

In the documentation of "Electrodialysis 0D" (https://watertap.readthedocs.io/en/stable/technical_reference/unit_models/electrodialysis_0D.html), an equation in Table 4 shows how the total resistance is calculated. This calculation is also used in the code.

The equation lacks a membrane resistance term at the end of the right hand side of the equation. For example, if n is the cell pair number and there are n AEM, there needs to be n+1 CEM; therefore, in the total resistance calculation, it needs "n+1*r_cem". Currently, it's "n*r_cem" in the equation. Adding a r_cem term at the end of the right hand side will fix this.

If the value of the membrane resistance is large or when the cell pair number (n) is small, the omission of the membrane resistance term can cause noticeable underestimation of the stack voltage and thus the power consumption.

Expected Behavior

No response

Steps to Reproduce

No response

Environment

• OS:
• Python:
• WaterTAP:

Anything Else?

No response

[ksbeattie]

@lbibl could you take a look at this?

[lbibl]

@yschang23 : Thanks for bringing this to our attention. Regarding the case in your comment, “if n is the cell pair number and there are n AEM, there needs to be n+1 CEM,” could you clarify whether you mean this as a special case or as a general requirement? My understanding is that the ED modeling literature we relied on, including the references cited in the documentation, counts CEM and AEM by the cell pair number. For cases like the one you suggested, a configuration with an end membrane can certainly occur, yet the end membrane is considered outside the repeating unit and its resistance is represented as part of the electrode-compartment resistance in the model and code. This is the common treatment in most of the ED modeling work I have seen. However, if you are suggesting that there must always be one more membrane of one type, and specifically one more CEM, I am not sure that this is generally accurate and would appreciate any support for this claim you could share.

Separately, if your goal is to represent practical stack behavior in more detail, you may also want to try the 1D ED model, which can better capture variations along the flow path.

[yschang23]

@lbibl could you take a look at this?

Hello! I realized this electrodialysis system was designed based on water splitting. Therefore, the water splitting products (H+ and OH-) on the electrodes react with the anions and cations from the feed, and that completes the ion current flow. It doesn't require an additional channel for circulating the electrolyte rinse. I got confused by some literature that utilizes the circulation of electrolyte rinse to complete the ion current flow. My bad.

With that clarified, the current resistance calculation is correct. There's no need to adjust.

[lbibl]

@yschang23 : I am glad this is now clarified. One additional note is that this ED model does not explicitly resolve the chemistry in the electrode compartments, including water-splitting reactions. Instead, it represents the net contribution of electrode-compartment processes, such as rinse-electrolyte circulation and electrode reactions, in lumped form through the constant electrodes_resistance term. For that reason, the model can also be applied to configurations where an electrolyte rinse is used.

With all clarified, I am comfortable suggesting that @ksbeattie close this issue.